Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
244 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#66627 | C2 | semidirect |
| 3. C2×#66558 | C2 | semidirect |
| 4. C3×C22⋊(C7⋊C8) | C2 | semidirect |
| 5. Dic3⋊(C7⋊C8) | C2 | semidirect |
| 6. (C2×D3)⋊(C7⋊C8) | C2 | semidirect |
| 7. Dic3×C7⋊C8 | C2 | semidirect |
| 26. C22⋊(C7⋊C8) | D3 | semidirect |
| 43. C3⋊(C7⋊C8) | D4 | semidirect |
| 78. C7×Dic3 | M16 | semidirect |
| 150. C3×C7 | #436 | semidirect |
| 181. Dic3 | #1136 | semidirect |
| 198. C7 | #4729 | semidirect |
| 217. C3 | #89784 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66627 | 2 |
| C4×C7×#67 | 2 |
| C2×#66558 | 2 |
| C3×C22⋊(C7⋊C8) | 2 |
| Dic3⋊(C7⋊C8) | 2 |
| (C2×D3)⋊(C7⋊C8) | 2 |
| Dic3×C7⋊C8 | 2 |
| #89784 | 3 |
| #4729 | 7 |